Lecture 1 quiz

Please write your name and NetID on a sheet of paper and answer the following questions (will not be graded):

1. Why are you taking the class?

2. What is the Taylor series for $1/(1+x)$?

3. What is $\partial r^{-2}/\partial x$ for $r^2 = x^2 + y^2$?

4. What is the solution to this linear system?

   $$\begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 3 \end{bmatrix}$$

5. Which matrix is positive definite?

   $$A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}, B = \begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix}, C = \begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix}$$

6. What is the complexity (using order notation) of the following?

    for i = 1:n
      for j = i:n
        v(i) = v(i) + A(i,j)*x(j)
   

7. Express in words what the previous code does